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<h1 class="title toc-ignore">6. Miscellaneous</h1>
<h4 class="author">Edzer Pebesma</h4>



<p><strong>For a better version of the sf vignettes see</strong> <a href="https://r-spatial.github.io/sf/articles/" class="uri">https://r-spatial.github.io/sf/articles/</a></p>
<p>This vignette describes a number of issues that did not come up in
the previous vignettes, and that may or may not be categorized as
“frequently asked questions”. Readers are encouraged to provide entries
for this vignette (as for the others).</p>
<div id="what-is-this-epsg-code-all-about" class="section level1">
<h1>What is this EPSG code all about?</h1>
<p>EPSG stands for a maintained, well-understood registry of spatial
reference systems, maintained by the International Association of Oil
&amp; Gass Producers (IOGP). “EPSG” stands for the authority,
e.g. “EPSG:4326” stands for spatial reference system with ID 4326 as it
is maintained by the EPSG authority. The website for the EPSG registry
is found at the epsg.org domain.</p>
</div>
<div id="how-does-sf-deal-with-secondary-geometry-columns" class="section level1">
<h1>How does <code>sf</code> deal with secondary geometry columns?</h1>
<p><code>sf</code> objects can have more than one geometry list-column,
but always only one geometry column is considered <em>active</em>, and
returned by <code>st_geometry</code>. When there are multiple geometry
columns, the default <code>print</code> methods reports which one is
active:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(sf)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">demo</span>(nc, <span class="at">ask =</span> <span class="cn">FALSE</span>, <span class="at">echo =</span> <span class="cn">FALSE</span>)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>nc<span class="sc">$</span>geom2 <span class="ot">=</span> <span class="fu">st_centroid</span>(<span class="fu">st_geometry</span>(nc))</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(nc, <span class="at">n =</span> <span class="dv">2</span>)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="do">## Simple feature collection with 100 features and 14 fields</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="do">## Attribute-geometry relationship: 0 constant, 8 aggregate, 6 identity, 1 NA&#39;s</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="do">## Active geometry column: geom</span></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="do">## Geometry type: MULTIPOLYGON</span></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="do">## Dimension:     XY</span></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a><span class="do">## Bounding box:  xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965</span></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a><span class="do">## Geodetic CRS:  NAD27</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a><span class="do">## First 2 features:</span></span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a><span class="do">##    AREA PERIMETER CNTY_ CNTY_ID      NAME  FIPS FIPSNO CRESS_ID BIR74 SID74</span></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a><span class="do">## 1 0.114     1.442  1825    1825      Ashe 37009  37009        5  1091     1</span></span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a><span class="do">## 2 0.061     1.231  1827    1827 Alleghany 37005  37005        3   487     0</span></span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a><span class="do">##   NWBIR74 BIR79 SID79 NWBIR79                           geom</span></span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a><span class="do">## 1      10  1364     0      19 MULTIPOLYGON (((-81.47276 3...</span></span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a><span class="do">## 2      10   542     3      12 MULTIPOLYGON (((-81.23989 3...</span></span>
<span id="cb1-19"><a href="#cb1-19" aria-hidden="true" tabindex="-1"></a><span class="do">##                        geom2</span></span>
<span id="cb1-20"><a href="#cb1-20" aria-hidden="true" tabindex="-1"></a><span class="do">## 1  POINT (-81.49823 36.4314)</span></span>
<span id="cb1-21"><a href="#cb1-21" aria-hidden="true" tabindex="-1"></a><span class="do">## 2 POINT (-81.12513 36.49111)</span></span></code></pre></div>
<p>We can switch the active geometry by using
<code>st_geometry&lt;-</code> or <code>st_set_geometry</code>, as in</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="fu">st_geometry</span>(nc))</span></code></pre></div>
<p><img 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" /><!-- --></p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">st_geometry</span>(nc) <span class="ot">&lt;-</span> <span class="st">&quot;geom2&quot;</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="fu">st_geometry</span>(nc))</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
</div>
<div id="does-st_simplify-preserve-topology" class="section level1">
<h1>Does <code>st_simplify</code> preserve topology?</h1>
<p><code>st_simplify</code> is a topology-preserving function, but does
this on the level of individual feature geometries. That means, simply
said, that after applying it, a polygon will still be a polygon. However
when two features have a longer shared boundary, applying
<code>st_simplify</code> to the object does not guarantee that in the
resulting object these two polygons still have the same boundary in
common, since the simplification is done independently, <em>for each
feature geometry</em>.</p>
</div>
<div id="why-do-dplyr-verbs-not-work-for-sf-objects" class="section level1">
<h1>Why do dplyr verbs not work for <code>sf</code> objects?</h1>
<p>They do! However, many developers like to write scripts that never
load packages but address all functions by the <code>sf::</code> prefix,
as in</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>i <span class="ot">=</span> sf<span class="sc">::</span><span class="fu">st_intersects</span>(sf1, sf2)</span></code></pre></div>
<p>This works up to the moment that a <code>dplyr</code> generic like
<code>select</code> for an <code>sf</code> object is needed: should one
call <code>dplyr::select</code> (won’t know it should search in package
<code>sf</code>) or <code>sf::select</code> (which doesn’t exist)?
Neither works. One should in this case simply load <code>sf</code>,
e.g. by</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(sf)</span></code></pre></div>
</div>
<div id="what-is-this-errorwarningmessage-about" class="section level1">
<h1>What is this error/warning/message about?</h1>
<div id="although-coordinates-are-longitudelatitude-xxx-assumes-that-they-are-planar" class="section level2">
<h2><em>although coordinates are longitude/latitude, xxx assumes that
they are planar</em></h2>
<p>Most (but not all) of the geometry calculating routines used by
<code>sf</code> come from the <a href="https://libgeos.org">GEOS</a>
library. This library considers coordinates in a two-dimensional, flat,
Euclidean space. For longitude latitude data, this is not the case. A
simple example is a polygon enclosing the North pole, which should
include the pole:</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>polygon <span class="ot">=</span> <span class="fu">st_sfc</span>(<span class="fu">st_polygon</span>(<span class="fu">list</span>(<span class="fu">rbind</span>(<span class="fu">c</span>(<span class="dv">0</span>,<span class="dv">80</span>), <span class="fu">c</span>(<span class="dv">120</span>,<span class="dv">80</span>), <span class="fu">c</span>(<span class="dv">240</span>,<span class="dv">80</span>), <span class="fu">c</span>(<span class="dv">0</span>,<span class="dv">80</span>)))), </span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>        <span class="at">crs =</span> <span class="dv">4326</span>)</span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>pole <span class="ot">=</span> <span class="fu">st_sfc</span>(<span class="fu">st_point</span>(<span class="fu">c</span>(<span class="dv">0</span>,<span class="dv">90</span>)), <span class="at">crs =</span> <span class="dv">4326</span>)</span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="fu">st_intersects</span>(polygon, pole)</span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="do">## Sparse geometry binary predicate list of length 1, where the predicate</span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a><span class="do">## was `intersects&#39;</span></span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a><span class="do">##  1: 1</span></span></code></pre></div>
<p>which gives a wrong result (no intersection).</p>
</div>
<div id="st_centroid-does-not-give-correct-centroids-for-longitudelatitude-data" class="section level2">
<h2><em>st_centroid does not give correct centroids for
longitude/latitude data</em></h2>
<p>Similar to the above, centroids are computed assuming flat, 2D
space:</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">st_centroid</span>(polygon)[[<span class="dv">1</span>]]</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="do">## POINT (0 90)</span></span></code></pre></div>
<p>where the centroid should have been the pole.</p>
</div>
<div id="dist-is-assumed-to-be-in-decimal-degrees-arc_degrees." class="section level2">
<h2><em>dist is assumed to be in decimal degrees
(arc_degrees).</em></h2>
<p>This message indicates that <code>sf</code> assumes a distance value
is given in degrees. To avoid this message, pass a value with the right
units:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>pt <span class="ot">=</span> <span class="fu">st_sfc</span>(<span class="fu">st_point</span>(<span class="fu">c</span>(<span class="dv">0</span>,<span class="dv">0</span>)), <span class="at">crs =</span> <span class="dv">4326</span>)</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>buf <span class="ot">=</span> <span class="fu">st_buffer</span>(polygon, <span class="dv">1</span>)</span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>buf <span class="ot">=</span> <span class="fu">st_buffer</span>(polygon, units<span class="sc">::</span><span class="fu">set_units</span>(<span class="dv">1</span>, degree))</span></code></pre></div>
</div>
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